Skip to main content
SpringerLink
Log in

Existence and Stability of Pseudo Almost Periodic Solution for Neutral Type High-Order Hopfield Neural Networks with Delays in Leakage Terms on Time Scales

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

Using the exponential dichotomy of linear dynamic equations on time scales, a fixed point theorem and the theory of calculus on time scales, we obtain some sufficient conditions for the existence and global exponential stability of pseudo almost periodic solutions for a class of neutral type high-order Hopfield neural networks with delays in leakage terms on time scales. Our results show that the continuous-time neural network and its discrete-time analogue have the same dynamical behaviors. Finally, we give a numerical example and simulation to illustrate the feasibility of our results. Results of this paper are completely new even if the time scale \(\mathbb {T}=\mathbb {R}\) or \(\mathbb {Z}\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Rakkiyappan R, Chandrasekar A, Lakshmanan S, Park JH (2015) Exponential stability for Markovian jumping stochastic BAM neural networks with mode-dependent probabilistic time-varying delays and impulse control. Complexity 20(3):39–65

    Article  MathSciNet  Google Scholar 

  2. Rakkiyappan R, Chandrasekar A, Lakshmanan S, Park JH (2014) Exponential stability of Markovian jumping stochastic Cohen-Grossberg neural networks with mode-dependent probabilistic time-varying delays and impulses. Neurocomputing 131:265–277

    Article  Google Scholar 

  3. Dembo A, Farotimi O, Kaillath T (1991) High-order absolutely stable neural networks. IEEE Trans Circuits Syst 38:57–65

    Article  MATH  Google Scholar 

  4. Liao XF, Yu JB (1998) Robust stability for interval Hopfield neural networks with time delays. IEEE Trans Neural Netw 9:1042–1046

    Article  Google Scholar 

  5. Xu BJ, Liu XZ, Liao XX (2003) Global asymptotic stability of high-order Hopfield type neural networks with time delays. Comput Math Appl 45:1729–1737

    Article  MathSciNet  MATH  Google Scholar 

  6. Xu BJ, Liu XZ, Liao XX (2006) Global exponential stability of high order Hopfield type neural network. Appl Math Comput 174:98–116

    MathSciNet  MATH  Google Scholar 

  7. Xiang H, Yan KM, Wang BY (2006) Existence and global exponential stability of periodic solution for delayed high-order Hopfield-type neural networks. Phys Lett A 352(4–5):341–349

    Article  MATH  Google Scholar 

  8. Ou CX (2008) Anti-periodic solutions for high-order Hopfield neural networks. Comput Math Appl 56:1838–1844

    Article  MathSciNet  MATH  Google Scholar 

  9. Yu YH, Cai MS (2008) Existence and exponential stability of almost-periodic solutions for high-order Hopfield neural networks. Math Comput Model 47:943–951

    Article  MathSciNet  MATH  Google Scholar 

  10. Xiao B, Meng H (2009) Existence and exponential stability of positive almost periodic solutions for high-order Hopfield neural networks. Appl Math Model 33(1):532–542

    Article  MathSciNet  MATH  Google Scholar 

  11. Park JH, Park CH, Kwon OM, Lee SM (2008) A new stability criterion for bidirectional associative memory neural networks of neutral-type. Appl Math Comput 199:716–722

    MathSciNet  MATH  Google Scholar 

  12. Rakkiyappan R, Balasubramaniam P (2008) New global exponential stability results for neutral type neural networks with distributed time delays. Neurocomputing 71:1039–1045

    Article  MATH  Google Scholar 

  13. Rakkiyappan R, Balasubramaniam P (2008) LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays. Appl Math Comput 204:317–324

    MathSciNet  MATH  Google Scholar 

  14. Liu J, Zong G (2009) New delay-dependent asymptotic stability conditions concerning BAM neural networks of neutral type. Neurocomputing 72:2549–2555

    Article  Google Scholar 

  15. Samli R, Arik S (2009) New results for global stability of a class of neutral-type neural systems with time delays. Appl Math Comput 210:564–570

    MathSciNet  MATH  Google Scholar 

  16. Samidurai R, Anthoni SM, Balachandran K (2010) Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays. Nonlinear Anal 4:103–112

    MathSciNet  MATH  Google Scholar 

  17. Rakkiyappan R, Balasubramaniam P, Cao J (2010) Global exponential stability results for neutral-type impulsive neural networks. Nonlinear Anal Real World Appl 11:122–130

    Article  MathSciNet  MATH  Google Scholar 

  18. Li YK, Zhao L, Chen X (2012) Existence of periodic solutions for neutral type cellular neural networks with delays. Appl Math Model 36:1173–1183

    Article  MathSciNet  MATH  Google Scholar 

  19. Bai C (2008) Global stability of almost periodic solutions of Hopfield neural networks with neutral time-varying delays. Appl Math Comput 203:72–79

    MathSciNet  MATH  Google Scholar 

  20. Xiao B (2009) Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays. Appl Math Lett 22:528–533

    Article  MathSciNet  MATH  Google Scholar 

  21. Wang K, Zhu Y (2010) Stability of almost periodic solution for a generalized neutral-type neural networks with delays. Neurocomputing 73:3300–3307

    Article  Google Scholar 

  22. Li X, Cao J (2010) Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity 23:1709–1726

    Article  MathSciNet  MATH  Google Scholar 

  23. Balasubramanian P, Nagamani G, Rakkiyappan R (2011) Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term. Commun Nonlinear Sci Numer Simulat 16:4422–4437

    Article  MathSciNet  MATH  Google Scholar 

  24. Balasubramaniam P, Kalpana M, Rakkiyappan R (2011) Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays. Math Comput Model 53(5–6):839–853

    Article  MathSciNet  MATH  Google Scholar 

  25. Duan L, Huang LH (2013) Global exponential stability of fuzzy BAM neural networks with distributed delays and time-varying delays in the leakage terms. Neural Comput Appl 23(1):171–178

    Article  Google Scholar 

  26. Liu BW (2013) Global exponential stability for BAM neural networks with time-varying delays in the leakage terms. Nonlinear Anal Real World Appl 14(1):559–566

    Article  MathSciNet  MATH  Google Scholar 

  27. Rakkiyappan R, Chandrasekar A, Lakshmanan S, Park Ju H, Jung HY (2013) Effects of leakage time-varying delays in Markovian jump neural networks with impulse control. Neurocomputing 121:365–378

    Article  Google Scholar 

  28. Li X, Rakkiyappan R, Balasubramanian P (2011) Exstence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. J Frankl Inst 348:135–155

    Article  MATH  Google Scholar 

  29. Peng SG (2010) Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms. Nonlinear Anal Real World Appl 11(3):2141–2151

    Article  MathSciNet  MATH  Google Scholar 

  30. Zhang H, Shao JY (2013) Almost periodic solutions for cellular neural networks with time-varying delays in leakage terms. Appl Math Comput 219(24):11471–11482

    MathSciNet  MATH  Google Scholar 

  31. Li YK, Li YQ (2013) Existence and exponential stability of almost periodic solution for neutral delay BAM neural networks with time-varying delays in leakage terms. J Frankl Inst 350(9):2808–2825

    Article  MathSciNet  MATH  Google Scholar 

  32. Hilger S (1990) Analysis on measure chains-a unified approach to continuous and discrete calculus. Results Math 18:18–56

    Article  MathSciNet  MATH  Google Scholar 

  33. Li YK, Chen X, Zhao L (2009) Stability and existence of periodic solutions to delayed Cohen–Grossberg BAM neural networks with impulses on time scales. Neurocomputing 72:1621–1630

    Article  Google Scholar 

  34. Gao J, Wang QR, Zhang LW (2014) Existence and stability of almost-periodic solutions for cellular neural networks with time-varying delays in leakage terms on time scales. Appl Math Comput 237:639–649

    MathSciNet  MATH  Google Scholar 

  35. Li YK, Wang C (2012) Pseudo almost periodic functions and pseudo almost periodic solutions to dynamic equations on time scales. Adv Differ Equ 1:1–24

    Article  MathSciNet  MATH  Google Scholar 

  36. Bohner M, Peterson A (2001) Dynamic equations on time scales, an introduction with applications. Birkhäuser, Boston

    Book  MATH  Google Scholar 

  37. Li YK, Wang C (2011) Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales, Abstr Appl Anal 2011, Article ID 341520, 22 pp

Download references

Acknowledgments

This work is supported by the National Natural Sciences Foundation of People’s Republic of China under Grant 11361072

Author information

Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, 650091, Yunnan, People’s Republic of China

    Yongkun Li & Bing Li

  2. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, Yunnan, People’s Republic of China

    Li Yang

Authors
  1. Yongkun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bing Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Yang, L. & Li, B. Existence and Stability of Pseudo Almost Periodic Solution for Neutral Type High-Order Hopfield Neural Networks with Delays in Leakage Terms on Time Scales. Neural Process Lett 44, 603–623 (2016). https://doi.org/10.1007/s11063-015-9483-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-015-9483-9

Keywords

Search

Navigation